Question

You are given the four points in the plane A = (-7,5), B = (-5,0), C = (-1,6), and D = (1,6). The graph of the function f(x) consists of the three line segments AB, BC and CD. Find the integral \displaystyle \int_{-7}^{1} f(x)\,dx by interpreting the integral in terms of sums of areas of elementary figures.